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8-1. Determine y for the area shown in Figure P8-1. y 2" 1" 2" 2" 4" 4" FIGURE P8-1 X

8-1. Determine y for the area shown in Figure P8-1. y 2" 1" 2" 2" 4" 4" FIGURE P8-1 X

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Problem Statement **8–1. Determine \( \bar{y} \) for the area shown in Figure P8–1.** ### Diagram Description **Figure P8-1** is a geometric diagram that outlines a composite shape. It consists of two main rectangular areas with the following dimensions and placement: - The full outer rectangle has dimensions of 5 inches in width (horizontally from left to right) and 10 inches in height (vertically from bottom to top). - The height is divided as follows: a bottom part measuring 4 inches, a middle section of 4 inches, and a top part measuring 2 inches. - The inner rectangle (which will be subtracted from the area) is centrally located. - Its dimensions are: width 1 inch (horizontally) and height 4 inches (vertically). - It is positioned 2 inches from the left side of the outer rectangle and 2 inches from the top. Both \( x \) and \( y \) axes are drawn with the origin located at the bottom-left corner of the outer rectangle. ##### Additional Notes: - The diagram includes various linear dimension labels to specify these distances, aiding in the understanding of the composite shape's distribution and balance. ### Determination of \( \bar{y} \) To find \( \bar{y} \), the centroid of the area, we consider the dimensions and positions of the entire shape and the inner subtracted area.
Transcribed Image Text:### Problem Statement **8–1. Determine \( \bar{y} \) for the area shown in Figure P8–1.** ### Diagram Description **Figure P8-1** is a geometric diagram that outlines a composite shape. It consists of two main rectangular areas with the following dimensions and placement: - The full outer rectangle has dimensions of 5 inches in width (horizontally from left to right) and 10 inches in height (vertically from bottom to top). - The height is divided as follows: a bottom part measuring 4 inches, a middle section of 4 inches, and a top part measuring 2 inches. - The inner rectangle (which will be subtracted from the area) is centrally located. - Its dimensions are: width 1 inch (horizontally) and height 4 inches (vertically). - It is positioned 2 inches from the left side of the outer rectangle and 2 inches from the top. Both \( x \) and \( y \) axes are drawn with the origin located at the bottom-left corner of the outer rectangle. ##### Additional Notes: - The diagram includes various linear dimension labels to specify these distances, aiding in the understanding of the composite shape's distribution and balance. ### Determination of \( \bar{y} \) To find \( \bar{y} \), the centroid of the area, we consider the dimensions and positions of the entire shape and the inner subtracted area.
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